### Journals Information

**
Mathematics and Statistics Vol. 5(1), pp. 5 - 18 DOI: 10.13189/ms.2017.050102 Reprint (PDF) (368Kb) **

## Bilinear Multipliers of Weighted Lorentz Spaces and Variable Exponent Lorentz Spaces

**Öznur Kulak ^{1}^{,*}, A. Turan Gürkanlı ^{2}**

^{1}Department of Banking and Finance, Gorele Applied Sciences Academy, Giresun University, Gorele, Giresun, Turkey

^{2}Department of Mathematics and Computer Sciences, Faculty of Science and Letters, Istanbul Arel University, Tepekent, Istanbul, Turkey

**ABSTRACT**

Let ω_{1}, ω_{2} be slowly increasing functions and let ω_{3} be weight function on ℝ^{n}. In section 2 we define a bilinear multiplier from L(p_{1}, q_{1}, ω_{1}dμ) (ℝ^{n}) × L(p_{2}, q_{2}, ω_{2}dμ) (ℝ^{n}) to L(p_{3}, q_{3}, ω_{3}dμ) (ℝ^{n}) by a bounded operator B_{m}, where 1≤ p_{1}, p_{2}, p_{3}, q_{1}, q_{2}, q_{3} < ∞ and m (ξ,η) is a bounded, measurable function on ℝ^{n} × ℝ^{n}. We denote the space of bilinear multipliers of this type by BM (L(p_{1}, q_{1}, ω_{1}dμ) × L(p_{2}, q_{2}, ω_{2}dμ), L(p_{3}, q_{3}, ω_{3}dμ)), and study of the basic properties of this space. We give methods of construction examples of bilinear multipliers. Similarly in section 3, by using variable exponent Lorentz space, we define the bilinear multipliers from L( p_{1} (x), q_{1} (x)) × L( p_{2} (x), q_{2} (x)) to L( p_{3} (x), q_{3} (x)) and discuss basic properties of the space of bilinear multipliers BM (L( p_{1} (x), q_{1} (x)) × L( p_{2} (x), q_{2} (x)), L( p_{3} (x), q_{3} (x))).

**KEYWORDS**

Bilinear Multipliers, Weighted Lorentz Space, Variable Exponent Lorentz Space

**Cite This Paper in IEEE or APA Citation Styles**

(a). IEEE Format:

[1] Öznur Kulak , A. Turan Gürkanlı , "Bilinear Multipliers of Weighted Lorentz Spaces and Variable Exponent Lorentz Spaces," Mathematics and Statistics, Vol. 5, No. 1, pp. 5 - 18, 2017. DOI: 10.13189/ms.2017.050102.

(b). APA Format:

Öznur Kulak , A. Turan Gürkanlı (2017). Bilinear Multipliers of Weighted Lorentz Spaces and Variable Exponent Lorentz Spaces. Mathematics and Statistics, 5(1), 5 - 18. DOI: 10.13189/ms.2017.050102.